* Treasury Wine sinks on plans to divert China wine over tariffs

* Australia demands apology from China after fake image posted on Twitter

* NZ shares post second monthly jump in a row

Nov 30 (Reuters) - Australian shares extended losses for a third straight session on Monday, as deepening tensions with its largest trading partner China following a move by Beijing to impose anti-dumping tariffs on Australian wine imports rattled investors.

The country responded defiantly on Friday to China imposing temporary anti-dumping measures, saying the "seriously concerning development" looks to be about diplomatic grievances and not any action by winemakers.

The S&P/ASX 200 index settled 1.3% lower at 6,517.8, erasing as much as 0.6% gains earlier in the session. This was the benchmark's worst fall since Nov. 4.

But it posted its biggest-ever monthly gain in November, buoyed by optimism around a swift economic recovery after the U.S. election outcome and COVID-19 vacine-related developments.

Import tariffs introduced by China were weighing on broader markets as investors reflect on heightened tensions between Australia and China, said James Tao, market analyst at CommSec.

"It's a bit testy at the moment. There have already been threats that there could be more tariffs, duties on Australian imports on other sectors as well ... If things get worse, you could see worsening political relations between the two (countries) which could spell negative for trade."

Tensions flared up further after Prime Minister Scott Morrison demanded an apology from Beijing about a Tweet containing a fake image of an Australian soldier holding the knife to the throat of an Afghan child.

Excluding tech stocks, all sectors ended in the red, with China-reliant miners and gold stocks leading declines.

Shares of Treasury Wines slumped up to 11.8% after it revealed plans to divert hundreds of thousands of cases of China-bound wine to other countries to avoid hefty tariffs.

Utilities and healthcare stocks helped New Zealand's benchmark S&P/NZX 50 index end 1% higher, its highest close in nearly two weeks. The bourse posted a second consecutive monthly gain. (Reporting by A K Pranav in Bengaluru; Editing by Rashmi Aich)